Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 6.6, Problem 63E
In Example 6.14, Y1 and Y2 were independent exponentially distributed random variables, both with mean β. We defined U1 = Y1/(Y1 + Y2) and U2 = Y1 + Y2 and determined the joint density of (U1, U2) to be
- a Show that U1 is uniformly distributed over the interval (0, 1).
- b Show that U2 has a gamma density with parameters α = 2 and β.
- c Establish that U1 and U2 are independent.
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Chapter 6 Solutions
Mathematical Statistics with Applications
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